{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quadratic Element for Poisson Equation in 3D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example is to show the rate of convergence of the linear finite element approximation of the Poisson equation on the unit square:\n",
    "\n",
    "$$- \\Delta u = f \\; \\hbox{in } (0,1)^3$$\n",
    "\n",
    "for the following boundary conditions\n",
    "- Non-empty Dirichlet boundary condition: $u=g_D \\hbox{ on }\\Gamma_D, \\nabla u\\cdot n=g_N \\hbox{ on }\\Gamma_N.$\n",
    "- Pure Neumann boundary condition: $\\nabla u\\cdot n=g_N \\hbox{ on } \\partial \\Omega$.\n",
    "- Robin boundary condition: $g_R u + \\nabla u\\cdot n=g_N \\hbox{ on }\\partial \\Omega$.\n",
    "\n",
    "**References**:\n",
    "- [Quick Introduction to Finite Element Methods](femdoc.html)\n",
    "- [Introduction to Finite Element Methods](http://www.math.uci.edu/~chenlong/226/Ch2FEM.pdf)\n",
    "- [Progamming of Finite Element Methods](http://www.math.uci.edu/~chenlong/226/Ch3FEMCode.pdf)\n",
    "\n",
    "**Subroutines**:\n",
    "\n",
    "    - Poisson3P2\n",
    "    - cubePoissonP2\n",
    "    - femPoisson3\n",
    "    - Poisson3P2femrate\n",
    "    \n",
    "The method is implemented in `Poisson3P2` subroutine and tested in `cubePoissonP2`. Together with other elements (P1, P2,Q1,WG), `femPoisson3` provides a concise interface to solve Poisson equation. The P2 element is tested in `Poisson3P2femrate`. This doc is based on `Poisson3P2femrate`.    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## P2 Quadratic Element\n",
    "\n",
    "For the quadratic element on a tetrahedron, the local basis functions can be written in terms of barycentric coordinates. The 10 dofs is displayed below. The first 4 are associated to the vertices and 6 to the middle points of 6 edges. \n",
    "\n",
    "Given a mesh, the required data structure can be constructured by\n",
    "        \n",
    "        [elem2dof,edge,bdDof] = dof3P2(elem)\n",
    "\n",
    "\n",
    "### Local indexing\n",
    "\n",
    "The tetrahedron consists of four vertices indexed as [1 2 3 4]. Each tetrahedron contains four faces and six edges. They can be indexed as\n",
    "\n",
    "    locFace = [2 3 4; 1 4 3; 1 2 4; 1 3 2];\n",
    "    locEdge = [1 2; 1 3; 1 4; 2 3; 2 4; 3 4];\n",
    "\n",
    "In `locFace`, the i-th face is opposite to the i-th vertices and the orientation is induced from the tetrahedronthus this is called _opposite indexing_. In `locEdge`, it is the _lexicographic indexing_ which is induced from the lexicographic ordering of the six edges. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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DJ/SDkaGRzqOdIjLjlhmGjBAToUlQHEGCpebePnfel+aJyJ///5+Pv3+8/9P+3/7Lb69+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\nYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "node = [1,0,0; 0,1,0; 0,0,0; 0,0,1];\n",
    "elem = [1 2 3 4];\n",
    "locEdge = [1 2; 1 3; 1 4; 2 3; 2 4; 3 4];\n",
    "showmesh3(node,elem);\n",
    "view(-14,12);\n",
    "findnode3(node);\n",
    "findedgedof3(node,locEdge);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boundary dof\n",
    "\n",
    "When implement boundary conditions, we need to find the d.o.f associated to boundary faces. For example, for Neumann boundary conditions, it can be found by\n",
    "\n",
    "               bdFace2dof = [elem2dof(bdFlag(:,1) == 2,[2,3,4,10,9,8]); ...  \n",
    "                             elem2dof(bdFlag(:,2) == 2,[1,4,3,10,6,7]); ...\n",
    "                             elem2dof(bdFlag(:,3) == 2,[1,2,4,9,7,5]); ...\n",
    "                             elem2dof(bdFlag(:,4) == 2,[1,3,2,8,5,6])];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A local basis\n",
    "\n",
    "The 10 Lagrange-type bases functions are denoted by $\\phi_i, i=1:10$. In barycentric coordinates, they are \n",
    "\n",
    "$$ \\phi_1 = \\lambda_1(2\\lambda_1 -1),\\quad \\nabla \\phi_1 = \\nabla \\lambda_1(4\\lambda_1-1),$$\n",
    "\n",
    "$$ \\phi_2 = \\lambda_2(2\\lambda_2 -1),\\quad  \\nabla \\phi_2 = \\nabla \\lambda_2(4\\lambda_2-1),$$ \n",
    "\n",
    "$$ \\phi_3 = \\lambda_3(2\\lambda_3 -1),\\quad  \\nabla \\phi_3 = \\nabla \\lambda_3(4\\lambda_3-1),$$ \n",
    "\n",
    "$$ \\phi_4 = \\lambda_4(2\\lambda_4 -1),\\quad  \\nabla \\phi_4 = \\nabla \\lambda_4(4\\lambda_4-1),$$ \n",
    "\n",
    "$$ \\phi_5 = 4\\lambda_1\\lambda_2,\\quad  \\nabla\\phi_5 = 4\\left (\\lambda_1\\nabla \\lambda_2 + \\lambda_2\\nabla \\lambda_1\\right )\\; ,$$ \n",
    "\n",
    "$$ \\phi_6 = 4\\lambda _1\\lambda_3,\\quad  \\nabla\\phi_6 = 4\\left (\\lambda_1\\nabla \\lambda_3 + \\lambda_3\\nabla \\lambda_1\\right )\\; ,$$ \n",
    "\n",
    "$$ \\phi_7 = 4\\lambda _1\\lambda_4,\\quad  \\nabla\\phi_7 = 4\\left (\\lambda_1\\nabla \\lambda_4 + \\lambda_4\\nabla\\lambda_1\\right )\\; .$$\n",
    "\n",
    "$$ \\phi_8 = 4\\lambda _2\\lambda_3,\\quad  \\nabla\\phi_8 = 4\\left (\\lambda_2\\nabla \\lambda_3 + \\lambda_3\\nabla \\lambda_2\\right )\\; ,$$ \n",
    "\n",
    "$$ \\phi_9 = 4\\lambda _2\\lambda_4,\\quad  \\nabla\\phi_9 = 4\\left (\\lambda_2\\nabla \\lambda_4 + \\lambda_4\\nabla \\lambda_2\\right )\\; ,$$ \n",
    "\n",
    "$$ \\phi_{10} = 4\\lambda _3\\lambda_4,\\quad  \\nabla\\phi_{10} = 4\\left (\\lambda_3\\nabla \\lambda_4 + \\lambda_4\\nabla \\lambda_3\\right )\\; .$$ \n",
    "\n",
    "\n",
    "When transfer to the reference triangle formed by $(0,0,0),(1,0,0),(0,1,0),(0,0,1)$, the local bases in x-y-z coordinate can be obtained by substituting \n",
    "\n",
    "$$\\lambda _1 = x, \\quad \\lambda _2 = y, \\quad \\lambda _3 = z, \\quad \\lambda_4 = 1-x-y-z.$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unlike 2-D case, to apply uniform refinement to obtain a fine mesh with good mesh quality, a different ordering of the inital mesh, which may violate the positive ordering, should be used. See [3 D Red Refinement](uniformrefine3doc.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mixed boundary condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%% Setting\n",
    "[node,elem] = cubemesh([0,1,0,1,0,1],1/3); \n",
    "mesh = struct('node',node,'elem',elem);\n",
    "option.maxIt = 4;\n",
    "option.elemType = 'P2';\n",
    "option.printlevel = 1;\n",
    "option.plotflag = 1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mixed boundary conditions. \n",
      "\n",
      " Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:     3600,  #nnz:    70718, smoothing: (1,1), iter: 12,   err = 2.83e-09,   time = 0.13 s\n",
      "\n",
      " Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:    30752,  #nnz:   659134, smoothing: (1,1), iter: 12,   err = 3.80e-09,   time = 0.38 s\n",
      "\n",
      " Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:   254016,  #nnz:  5674430, smoothing: (1,1), iter: 12,   err = 3.57e-09,   time =  2.2 s\n",
      "Table: Error\n",
      " #Dof        h        ||u-u_h||    ||Du-Du_h||   ||DuI-Du_h|| ||uI-u_h||_{max}\n",
      "\n",
      "   729   2.500e-01   5.00700e-03   1.32387e-01   5.25032e-02   1.21275e-02\n",
      "  4913   1.250e-01   6.03477e-04   3.52893e-02   9.25606e-03   1.61600e-03\n",
      " 35937   6.250e-02   7.43413e-05   9.04712e-03   1.42917e-03   2.02649e-04\n",
      "274625   3.125e-02   9.26851e-06   2.28115e-03   2.17441e-04   2.52582e-05\n",
      "\n",
      "Table: CPU time\n",
      " #Dof    Assemble     Solve      Error      Mesh    \n",
      "\n",
      "   729   1.10e-01   2.00e-02   1.20e-01   1.00e-02\n",
      "  4913   1.90e-01   1.30e-01   1.00e-01   1.00e-02\n",
      " 35937   8.80e-01   3.80e-01   3.90e-01   7.00e-02\n",
      "274625   6.22e+00   2.17e+00   3.01e+00   0.00e+00\n",
      "\n"
     ]
    },
    {
     "data": {
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YzpN4e8iQITwlnTp1Gjly5KJFi/744w/DTmHc1rT3nNB+hGO9xKGCmDMylnDg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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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44F0AYO/l0t1fkn/5G+3pBwwwiaup4RMpCmgZW/bdOMnzLzP3ciszT5u+HU95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1ezNgz/Nmfd1jJ+qGuHatNGGRhhSHTatGF+gb4ORy6UI8R9M+/ihrnt1UrHEgAEcDz+mpfKbdvs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\nAIAIBBIAQAQCCQAgwn8Bhd7AvNtPJUgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Non-empty Dirichlet boundary condition.\n",
    "fprintf('Mixed boundary conditions. \\n');    \n",
    "% pde = polydata3;\n",
    "pde = sincosdata3;\n",
    "mesh.bdFlag = setboundary3(node,elem,'Dirichlet','~(x==0)','Neumann','x==0');\n",
    "femPoisson3(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pure Neumann boundary condition\n",
    "\n",
    "When pure Neumann boundary condition is posed, i.e., $-\\Delta u =f$ in $\\Omega$ and $\\nabla u\\cdot n=g_N$ on $\\partial \\Omega$, the data should be consisitent in the sense that $\\int_{\\Omega} f \\, dx + \\int_{\\partial \\Omega} g \\, ds = 0$. The solution is unique up to a constant. A post-process is applied such that the constraint $\\int_{\\Omega}u_h dx = 0$ is imposed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pure Neumann boundary condition. \n",
      "\n",
      " Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:      729,  #nnz:    13921, smoothing: (1,1), iter: 11,   err = 8.36e-09,   time = 0.06 s\n",
      "\n",
      " Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:     4913,  #nnz:   103105, smoothing: (1,1), iter: 12,   err = 3.57e-09,   time = 0.07 s\n",
      "\n",
      " Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:    35937,  #nnz:   792961, smoothing: (1,1), iter: 12,   err = 3.77e-09,   time = 0.35 s\n",
      "\n",
      " Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:   274625,  #nnz:  6218497, smoothing: (1,1), iter: 12,   err = 4.84e-09,   time =  2.2 s\n",
      "Table: Error\n",
      " #Dof        h        ||u-u_h||    ||Du-Du_h||   ||DuI-Du_h|| ||uI-u_h||_{max}\n",
      "\n",
      "   729   2.500e-01   4.33972e-03   1.06671e-01   1.11359e-01   2.69023e-02\n",
      "  4913   1.250e-01   5.63932e-04   3.20352e-02   2.08121e-02   5.72678e-03\n",
      " 35937   6.250e-02   7.20239e-05   8.63820e-03   3.68308e-03   8.55523e-04\n",
      "274625   3.125e-02   9.12740e-06   2.22998e-03   6.44578e-04   1.14993e-04\n",
      "\n",
      "Table: CPU time\n",
      " #Dof    Assemble     Solve      Error      Mesh    \n",
      "\n",
      "   729   1.00e-01   6.00e-02   4.00e-02   1.00e-02\n",
      "  4913   1.60e-01   7.00e-02   9.00e-02   2.00e-02\n",
      " 35937   8.10e-01   3.50e-01   4.20e-01   7.00e-02\n",
      "274625   5.80e+00   2.21e+00   2.78e+00   0.00e+00\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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EBgYuXLhQKc1K0nGp+v9JYoXKjkNCrzoKNuH2TQSSGpD6TmfsOwCQVTVPfXEk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\nWvj/0IPcG09yS4gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Pure Neumann boundary condition.\n",
    "fprintf('Pure Neumann boundary condition. \\n');\n",
    "pde = sincosdata3Neumann;\n",
    "option.plotflag = 0;\n",
    "mesh.bdFlag = setboundary3(node,elem,'Neumann');\n",
    "femPoisson3(mesh,pde,option);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Robin boundary condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Robin boundary condition. \n",
      "\n",
      " Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:     4913,  #nnz:   105409, smoothing: (1,1), iter: 12,   err = 2.66e-09,   time = 0.05 s\n",
      "\n",
      " Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:    35937,  #nnz:   802177, smoothing: (1,1), iter: 12,   err = 4.68e-09,   time = 0.35 s\n",
      "\n",
      " Multigrid V-cycle Preconditioner with Conjugate Gradient Method\n",
      "#dof:   274625,  #nnz:  6255361, smoothing: (1,1), iter: 12,   err = 8.75e-09,   time =  2.4 s\n",
      "Table: Error\n",
      " #Dof        h        ||u-u_h||    ||Du-Du_h||   ||DuI-Du_h|| ||uI-u_h||_{max}\n",
      "\n",
      "   729   2.500e-01   4.44278e-03   1.19113e-01   8.29341e-02   4.13848e-02\n",
      "  4913   1.250e-01   5.66084e-04   3.35620e-02   1.48538e-02   3.95143e-03\n",
      " 35937   6.250e-02   7.20911e-05   8.82519e-03   2.51203e-03   3.51203e-04\n",
      "274625   3.125e-02   9.13225e-06   2.25306e-03   4.25087e-04   4.30278e-05\n",
      "\n",
      "Table: CPU time\n",
      " #Dof    Assemble     Solve      Error      Mesh    \n",
      "\n",
      "   729   7.00e-02   1.00e-02   3.00e-02   0.00e+00\n",
      "  4913   1.60e-01   5.00e-02   9.00e-02   2.00e-02\n",
      " 35937   8.30e-01   3.50e-01   3.80e-01   7.00e-02\n",
      "274625   6.04e+00   2.36e+00   2.94e+00   0.00e+00\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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PDthfcDMoEsqPwBWIQWoZWxy+Gzx48A8//KC9zX1st+ZWQKVq1itCG1Kpdj8J\ne3CI3HOLpRyKhPIjcAJikAwjfWrPLMkU7g/fMdX8eLtfv358NR06dHjmmWfmzp37999/G3cK05am\nv+YEFuRyCGOTIlAUhIVp95OQLlRxp5h9NbeIeBUiWB9HMUgGqez0INxysS4vO1syteLmOZMUaEka\nGho8PT3Xrl27du3axYsX+/n5JSUlDRo0SC6XW70062KTKrt791hnjEClYk9v7CcF6vQwIiGiO4KV\ncZR1SIaq7HQh6ObrE7O/VLEvN2GxR9h0/YtnOUjnzp2XL1+Ov964cWP8+PGLFi166aWXunfvbt3S\nrEh0dHR0dLSN2aRevYCiWGwPRek5SDzU+15hlc7lChEACgCFup9EQvnZEThAH5dxlB6SCUGLZz3C\nphfsi8uSTLF2ddrEgAEDVqxYUVJSsmvXrtLS0iFDhmzbtg3vXbdu3ahRo4wrDQDaXiBBH2IxJCez\n70pOBolE13H6Fs9RRHRnt9jE2gZikIwELZ6ty8s2VYExR5XoY6oCW8lrr70GABkZGfX19ampqQ8f\nPsS7srKyrl69alxpAGCSAgn6oCiQSlkS9XaSMMJYtmFnqrnAQW5czQgEYyAGyXjQ8J1JilIVVskv\n50iPKeWXcyzsqtXb25vH4ymVpjGEpi2N0DISCSiVzSyQSgUKRYvHqQqrUMBJln2UerBORUL5ESyK\no8whmQmTLE6K3HNbcacI2yFh7DlpuNBiTolqa2tpmvbw8NCT5+7du/v3N5ne0aNHjx492ujSCCaG\nokAiif/ww+iJExtV4JGR0NI7ARI4iId6s+8WA9wDkBJPdwSLQnpIVkZVWCVPaeoVoQ3pMaXF+kkq\nlQoAevXqpSfP7du3lzM4fPhwW0ojmB6xOMHLC2QyEIkA1OuTWjxIlzVCSADEAEBEdwTLQXpIJkae\nkhNzrK0DVpSnS9g3qQYdYnT42sTERAAYOHCg9q6SkhK0ER4eXlBQgNNdXV2NKI1ZIMFcyGQgFAIA\nxMSAWNzKg4Sx55IXDEaRJ5shAVAR0R3BcjiKQYqPjzeV8ls/9wqr2t65sVj36MyZM3FxcU899dTM\nmTPRKlSsw6mpqTl9+jTaFggEnp6eBpUGAG5ubroK5Bo2oYhtFUjmgJw1REaCrGUbghpb2DepypVa\nAkgKQAYQBqACkANQADq1ewSCCXAUg2QZawQAvTxdWN409aJtfgwtofUUFBR8/vnnAFBbW3vlypWD\nBw+6u7tv3ry5Xbt2ABAQEPDzzz8HBwf7+/vHx8dnZma6uOirif7S2rdvr6vA+/fvJyUlRUdH83g8\nM12pQdjkOiRdREQ0ziQpFKBQNA7i6QZ5cBDGnovcc1s2M1BrN0CyOpSfHCCUwXJBdgAAIABJREFU\nhPIjmBPaAfD39+ds4cqCSljyh8aHWnNWWVDZlmL9/Py2bNmisR0Y2PR34+7uPmTIkMjISJVKhY86\nceJE165dAYDH44lEoiVLlri7u+s6RYul6Snw1KlTAFBXV9fKmmtgpgdq1nZibppVPjmZBqABaIpq\n5eGySw9gyR/SI3d17KZpoGmgaYqmlW2sKcGacLyRO0oPibNQni7ScKG0+bSTJFxojk7SrVtsjjUZ\nPP/88zk5OXfu3OnevXunTp0AIC4uzujSDC2QYDJEIhCJQKFoVDe0YjIJeXCQX84JfbqzyK+L1m6G\n6C4MgKj6CeaBqOysj2S8ULlyFLJAlKcLHTe2BfmTOXFycvL390fGw9wFrlq1ytPT093dfd68eXV1\ndaY6o2Myu1t1s+949igmRpdrOw0k44Uivy7sISqAhPIjWAJikDgB5ekiCRdKw4WScAeKiX7+/PnD\nhw8nJCTs2LHj119/tXZ1bJjavKxZ3WtKk/c1JVFUo01SqXRFktUGNT/23jlFvAoRzA4xSFxBPNRb\nMl5oqr7Rp59++txzz2lvc4r//Oc/w4cPj4yMHDBgwN27d1GiTdScawi6+f5RJCjY13w4FA3cAYBc\n3hrfDQBAebqwaO2adpNQfjaMTbi0JwbJPpk1a1b//v21tzlF79690Ya7u3t9fT3atomac5Ddee0A\n4GHCoqYkimpysRppolE2irEaSU68CtkSxLkqgaAPjmi+7YO8Gr7X9KWVN883i9SFO0mt892AiTmq\nFMaeU9wpYtknJqH8COaCGCQCwU7wCJvu3M0nN2Fxs1TD1Q2gFjiwyO0ad5NQfgSz4CgGyVQRYwkm\ngc/n83g87vSQbGJ4vTX0iNpQ+yir7eoGAGBZJMuEiO4IZoBH07S162B2AgICzDd4atbCCayY6Z7b\n9KPElS/YF6cZyBi5EUK6huTkFn03tBaV2qsQAEiJVyHbgOON3FF6SASCg6BpjaBN6gbFnSLe0pPs\ncSOp5qH8FAYVTCCwQAwSgeAAMNUNhgzcify6SMOF8ss57AIHihHKjwgcCG2GGCQCwQ7JkkxRLhje\nLAmrG5Dr1VbTggcHMRE4EEwGMUgEgh2C1A3NkoxVNwByrthFd4yuCBLKj2AaiEEiEOwQQTdf//0P\nNFMN992AoDxdZDP7AUDknttsuwEkatGdgojuCMZDDBKhrdy9exeFk2AlNTU1KSkpNdWwALgEs9AG\ndQPl6SKbGShPydEpcCCe7ghthhgkQpuoq6tbuHDh+vXrtXfV19dPmjRp9OjREokE+ayzfPUI6VN7\nNluWJBI1RqMwfOAOCRwk43X4/6WI6I7QVohBIhiPWCx++umnDx8+zLr3xx9/PHLkSGpq6o0bN44d\nO7Z9+3aFIcNEBJPgIZqu6XQVd5IMVDcAgE5rhKCI6I7QJohBIhjPqFGjPvzww7Fjx7LuvXTp0siR\nI1Fg2bCwsMDAwOPHj1u2ggTwmr609lGWptNVY9UNGGHsOfYdYiK6IxgPMUgE43nnnXcWLlwYFBTE\nurdz584PHjxoaGgAgJqamvz8/MzMTMtWkACCbr49ojbodLpqoLoBgfTf7AIHIF6FCMZDDJKd09DQ\nkJ6efvny5cLCQgufetq0aXfu3BGLxb/88suMGTPy8/MrKiosXAcCsDpdbVtkCsrTJXnBYJ3O7igi\ncCAYCTFIdktZWdncuXM7deoUEBAwdOhQLy+v8ePH37hxo/UlFBUV8fn8tWvXGleBwYMHHzx48MGD\nB5988kmfPn0mTpzYvXt344oitAY9HoRZnK62Qd0AuqLKNu0mofw4h014EHYUg+Ro3r7z8/OHDBmy\nc+fOadOm7dmzZ/fu3W+88UZycvLzzz+vMmQem6Zpo93vpqenV1RUnDhx4vr16+vWrUtNTe3bt69x\nRZkbm/ittkh0dLSuXYJuvl7Tl5pQ3YARxp5j9+BAkVB+3IIE6OMQen6rdsnatWszMjISEhK2bds2\nY8aMWbNm7dy588MPP8zLy9uwYYNZTx0VFbV7924AcHNze+ONN3744YeSkpLPPvvs4cOHM2bMMOup\njcYmfqttxEM0XfjNxWZJbVY3qAqr9HlwEJNQfgTDcBSD5FCUlZVt2bKlf//+UVFRzPSVK1dOmzbN\n0ChE+fn5M2fO7Nixo7u7+6RJk3JzczUyaBS4ZcuWM2fOAICPj8/nn3/+6aefdu7cecOGDfv27SND\ndlZE0M2XJbVt6oYWPDgACeVHMBDaAfD397fRwo3j8uXLALB69eo2loN1EH5+fsuWLUPy7tmzZxta\nTk5OThtrooGZ7jkHH2XraX3l784f1ux7cjINQAPQFGXcqZUFlbDkD+mRuzp207SIpoGmgabFxp2B\nYDI43shJD8kOycjIAACKokxSmre3d2pq6hdffPHHH38MGDBAj5cgXfTo0cMkNSG0ndq8rNpHWc0m\nk9qmbgC1VyHpMaU8JYdtNxHdEVqLs7UrYG/U5mWxpuMBE5RB46sJ8wMAWvpTV1dnYN3ZmTp1qoeH\nB9oeM2aMXC43SbEEq4CWJXmETW+WKpEAeqxyOUREgOGvMuKh3vcKq2KOKUV+XVgEeBRAMgBy8iAH\nCFUvVCIQmkMMkokpVezT1DIBAAB2vax8b7j2VxPmB4DevXsDgFLJ4gRz9erVKpVq27ZtLV+JGmb/\nhs8nXWqbR9MagVrdEBnZ2EnCkZMMIWKot+JOkU45OAUgU0sbIgGS1X0mAoEBMUgmxkM03UOk9YNn\nINxyUc/XtucHAH9/f4FAsGfPnpiYGKbioK6u7uuvv0a+fIyGNlYFTuAaFTfPufUf1fgFqRsUisZO\nElI6GALl6ZL83mB9OcQA9wCkaoGDkjF8J9F5EMGhIAbJxLBrmXRnMHl+APD09Jw3b97WrVu//vrr\nJUuW4PSvvvqquLj4xRdfbLEEgt3zMGFR5c3zTUJw5LsBCe0iI4Gte20CIgBUAHK1TVIBqNThlAgE\nIvu2V1atWuXt7b106dJ58+YlJib+/vvvCxYsWLFiRZ8+fZYtW8bMqT+aEcFeYXG62mZ1A0KeksNb\nelKnwEGiHqxTkJVJBE2IQbJPKIq6evXqK6+88tNPP82ePXvChAnffffdlClTTp486erqirPpiWYE\n6hkjJycnZgrzK8F2YXe6agrfDeKh3tJwoXioN/tuikwgEXRCDJLd0r1794MHD5aVlf31119Xr159\n/PjxTz/95OPjgzPoj2YEAJ06daJpevny5Thl06ZNjx8/Nm+9CZaC3ekq9t3QhoCK+sImydWDdUyE\n6g8RhTs2xCDZOc7OzoMGDQoKCnJzc9PYpT+aEcERYHe6ihQNCoURvhta5p6WNVIxPgTHhhgkx0V/\nNCOCI4Cdrjatb8OdJDAmMgUTVWEVb+nJmKPN9RG9ACj1h4l2CsHxIAaJQHBo0CqFZupNijKJugF7\ncGhmk8QASvWHYuQWASiJ3M7RIQaJQHBoBN18Nb2Ag2nUDaAWOMgv5yjuFLWQVU4mkAjEIBEIBG1M\npG4AgIih3lQXl8g9t9nDJjGRk7BJjg4xSAQCAQAgfWpPTaerplA3MEJU3NLch4JTyNSh/FQkbJKj\nY/MGiabpzZs3v/DCC2FhYZs2bbJ2dWwPQ8MjEeyVHlEbmsntTKduoDxdkhcMVtwp1hQ4iAEkAOLm\nofxI2CQHxuYN0rFjx/bv3//dd9/95z//2bt374kTJ6xdIxvjyy+/PHTokLVrQbA+rv1HsoSUxeqG\nNtsk2cxAfeuTItQuwFUAbToVwYaxeYP0zz//TJ06tXfv3n369AkKClK1YQKWQHBk2N0kYnVDm5cl\n6fTdgKBI2CSC7RukqKgoFKg7LS3t3Llzw4YNs3aNCATbRrmAEeKEqW5ogwSciTD2HLvAgQJIVm/L\nicDBEeGcQcrKyrp06RIzJSMj48iRI1evXkVx5wDg8OHDS5YsWbJkyYYNGwCApundu3fPmTNn2bJl\ngwYNskKlCQR7AYWUbeZ0VSw2oe8GZIrCvkll300RgYNDw63wE/X19atXr+bz+bijs379+m3btgmF\nwuzs7KCgIJlM5uTkJBQKQ0NDAcDLy6uuru79999/9OjRrl27/P39rVp9AsEs0DS9ZcuWX375pa6u\nbvLkye+//775zoWcrhbsi2sWLUkmA6EQwASRKZDAQWccP2ALm0RwGDjUQ1qxYsW4ceNOnz6NU1Qq\n1datW9esWfP7778nJSVduXLlwIEDANC3b99JkyZNmjQpJCQkMTGxpKQkMTFRvzUKCAgICAiIj483\n+2UQbIr4+PgANdaui04srNxx7T/SuZtPMwm46dQNAKDPGiGIwMFR4ZBBCg4Ofuutt0aMGIFTLl68\n6O7uPnnyZADo06fP8OHDL1y4oHHUqVOnrl27NnTo0ODg4ODg4L1797IWnpaWlpaWFh0dbb76c4qy\nsrLa2lrtbXs9r9FER0enqbF2XXRiYeUOjkzRTAUukQBFAZjS6aow9hy7BweKCBwcFA4ZpBkzZsyZ\nM4cZYDs3N/fJJ59EUXkA4KmnnsrLy9M46ocffrh58+ZVNTNmzLBcjTnM4MGDf/jhB+1tez2vfWN5\n5Q52utqUhELKgsnUDarCKn0eHCj1ZBIQgYMDwSGDpE1DQwMzHJyzs3NdXZ0V62ND0DTNum2v57Ut\nbEK5g5yu6lQ3yOVtLB97cNApcBAxVssSgYNjwGmDJBAIqqqa3p4qKiratWtnXFFk9oigBzSTZJlz\nIeXO1q1bccr69etfffXVTZs2RUREiMXi+vp6AEDKndDQ0Geffbauri4qKuq///3vrl27Zs+ebZl6\nok5Sj4UbmqVi3w2m6CQhgYOqsCpyz232HJLmNolg73DaIPXs2TMzM7OyshJ9TU9Pf/LJJ40rynFm\njwhGgGaSLHAi21LueIRN10wyqboB1B4c5Ck5ml6FMFjgoCCTSUZiE8odBKcNUkhIiJOT07p16/Lz\n8/fs2XP9+nUS3tRoSktLhwwZsm3bNpyybt26UaNGtT0zofXYqHKn2WSSqdUNLYSooBiTSVJik4zB\nJpQ7CG6tQ4Lmvj67du0aGxsbExOTmJjo5OT09ttvi9AQtj0Sox4DkUjMEqSsvr4+NTX14cOHOCUr\nK+vq1attz0xoPUh0k52drVSv5tFW7ty7d0/jKOtqQwr2xZUm7/MQTW/0LYTUDZGRjeoGU/wkJeOF\nqqIqkV8X9t0UQLLa6aocIFTdZyLYHZzrIS1fvvy7777DXydOnHjp0qVTp0799ddfy5YtM7pY7s8h\nyeVyqVQqb/NcMcEILDmHpAH3lTseounO3XyaebozqboBIZsZqG+3iEwmOQSc6yFpw+fze/To0cZC\nyBySHu7evbt//378dfTo0f369bNifSxPdHR0dHS0VWySCZU7ZkLQzdc3JkkzFftuiIlpnFUyEZF7\nbrMbJwmACkCu9uCQzJKFYOtwrodEsDy3b99ezuDw4cPWrpEDYULljkWHASgKpFIAk6kbEIo7RfoE\nDhIicDAeKw4DtB4b6CHZFnK5PMYoRSxefi8U6o4ZoxuxWGzo5FNJSQnaCA8PLygowOmurq7Md3aN\nzATTgpU7CxcuPHHixPXr1xcuXGhcUeYeBkif2tNDNL1JCB4RAXI5qFSN6gZTTCaJ/LpIw4U6wyZR\nADIAtFMK0AtA3PZzOgpWHAZoPcQgmZh79+61xbOL+bzCuLm5AQCW2dTU1GDxsUAg8PT0ZGZGc+ys\nmQltx0aVO5pOV82gbgAAfUH8QG2TUJcsBoAiAge7wlEMUnx8vGWmkXr16kUhUayBYFNk3OEt0r59\n+4CAgJ9//jk4ONjf3z8+Pj4zM9PFhd3Npf7M9+/fT0pKio6Otpvw5/Hx8QkJCRY73fLly5lfJ06c\nOGHChLy8PC8vL4FAYLFqGAp2uuoWo14AIBbD9u2NPSS53LSTScLYc8qVbCsNxAx34JHEHbh9QTsA\n/v7+3C8c2SGKokxSmp+f35YtWzS2T5w40bVrVwDg8XgikWjJkiXu7u66StCT+dSpUwBQV1fXyvOa\nHDM9ULO2E3NjmcrX5GamTfEuObm3KUmppAFoANpETbex1IJKWPKHOPGWzhximgaaBpoWm/C09g/H\nGzkRNTgQzz//fE5OTlpaWlFRUXJyclxc3OPHj02SmcAFLCBqEHTz9RBN13S6agZ1A+XpkvxecAsC\nBwoAiDvw1mITogZikBwLJycnf3//Tp06tT3zqlWrPD093d3d582bx7WlM46JZQalvaYvBQ2nqxER\nJo9MAWqBgz4PDlj5LQWQm+q0dovF/GO1BWKQuIJEIpFKpWZy02AOzp8/f/jw4YSEhB07dvz666/W\nrg7BQiCnq6UKRqgkU0emwEjGC8XPercqREUMcQduF1h7zNAS+Pv7b9q0yXyFm6nktrB79+4bN25o\nb5sENIeUlpaGvg4YMOCLL76wwHkxJr/nmzZt8vf35+ajbCXWr7xI1DiZJJOZsFRlQaVo8xVqzVmd\nOaTqySRTzmHZLdZvJ3pxlB6So3lqmDVrVv/+/bW3TUjv3r3Rhru7O4qYYJnzmgObGM3gOiaNTIHB\nYZN0hqgg8c7tCEcxSASTYzeab4LRKBcMr83LavxiHnUDqENU6HR2R5F45/YDMUgEgp1gYQ/CtXlZ\naFlSU5J51A0AoNMROIJiCBzkJN45O0RlR7BP+Hw+j8cjPSSuYeFxaZaQsmZTN2CEsedaEDioSLxz\ndmxiXJoYJILBhISENDQ04BA+Fy5cWLFihXWrRLAKjT6EmJghMgVGVVhFdXEJ+yaVfbeYEaIizLRn\nJlgIOzdIMTExMTExTM+hBALB5DRblmQedQOoBQ7s/oQQROBg49i5QUJR70pLS7kfoI9gRWxieJ2z\nlCbvq7x5vuLmucbvZlM3AADlye59Ub2bCBxsGzs3SBhHk30TDMImhtc5C3a62pRkNnUDhrf0pDwl\nh2UHRQQONoyjGCQCwe6x1jCAoJtvj6gNlTfPlyar3Tcw1Q2m7iQhpOHCmGNKInBoPTYxDGCHBkku\nlwvVMKPeIYyLnkcgcB8rDgOwOF3F6gaVyuTqBgCIGOpNBA4GYRPDAHZokFCIPARKqa2t1UghmIrL\nly/v3bs3JSXFwudlfzUmWA8Wp6tmUzcA8eBgp9ihQUIh8hAau8wU+85hmTFjxpgxYz755JNhw4ZN\nmTKFpmmLnTrsm1SdgQkI1gAtS7KYugFQiIoFg3WGqKCIwMH2sEODJBaLlWo0LJBIJLIhd9oc5+TJ\nk0lJSefPn09PT09MTPz555+vXr1qsbOrCqukx5TEJnEKj7Dpzt18mi1OMrO6AXkVkh5TEoGDfWCH\nBokVFBlaLpeTOSRTkZ+fP3PmzKCgIAAYOXIkAFRVWXoYTXpMqXPpviHYxHyvTeAbk9TsO0U1DtyZ\nTd0gHuotDReKh3qz76aIwMGWcAiDJBAI0tPT0bZUKiU2ySRMnz59586dubm58fHxr732Wnh4+IgR\nIyx2duXKUWhJiqqwKuybVPYX5FZjE/O9topIZFZ1AwBIxgv17RYTgYPNYOcGCUW98/LyoigqObmx\n9y6XyxXmWRvBQRoaGtLT0y9fvlxYWGiO8ouLi5OTk/Py8urr6x8+fGiOU7CC5g+wTYohw3dcQrlg\nuE51gzmFRWFbdIjuiMDBVrB2QCZLgGNSydQ/DIqilEqlaQvnGqWlpXPmzOnQoQN+1uHh4devX299\nCYWFhTwe77PPPmsxZ1lZGUVR//73v9tQXwPA91xZUCk9cheW/IE+os1XTFKsLWLWKJSGUn7jbNoU\n72ZJUmlj+D6x2EwnVRZUwpI/pEfu6thN05Q6lJ/UTFXgNDYRhdLOe0gaiMViqVQKACqVKiwszI5V\n4Pn5+UOGDNm5c+e0adP27Nmze/fuN954Izk5+fnnnzfoqlErYd319ttvP//882i7Q4cOgwYNsvyo\nF+XpIhkvlIY3jtgo7hSbZErJRuGOOxK3/qP89z9oloTVDXK5mXw3IIGDzuE7ytEFDjYxLu1YBgkA\nIiIixGIxqG2StatjLtauXZuRkZGQkLBt27YZM2bMmjVr586dH374YV5e3oYNG1o+vhWMGDFCoVBs\n27attLT0wIEDx44dCw0NNUnJhiIZL9SYUiLDd5wDqxsAzKRuAACd0obGOhCBA9dxOINEUZREIhGJ\nRACgUqkizfbbsCJlZWVbtmzp379/VFQUM33lypXTpk0zNI4RUtN17NjR3d190qRJubm5KP3NN99c\nsGDBu+++26lTp2nTps2fP//dd9812TUYCJpSQl0logjnDsoFw5uWJZlf3YDR2VEWE4EDt7HuiKFl\nuCEX1pdnMVOYS5Sk0jaNKHNwTPby5csAsHr16jaWg3UQfn5+y5YtGzt2LADMnj2bmae6ujozM7Om\npqaN5zIIPfecOaVErTmrLKg0SbHch4OVr8nNzPz365n/fr0pSalsnEmiKNpEk7jaKAsqqTVndU4o\nKmlapJ5MMtd8FnfhYDthYv89pIaK7JxCKD03i5nIFN3ZnxA8IyMDTOeWwtvbOzU19Ysvvvjjjz8G\nDBhw6tQp5t527dr5+vqiZV5cQHv4ro2KcILRsDtdxcuSYmKaPiYFdZcVd4qJBwebw/4NEt/NZ81e\nZwAoPatpk7DozoRC8IaKbNaPRgbz5QeAhoYGAKirqzPJFU2dOtXDwwNtjxkzxkzycUNp5sezOUQR\nzh1YnK7igTu5HKRSkEpBLje5Fhx7cNBpkxxb4MBZnK1dAUuQU8Tbnjp6bt+95VeXuQevx+lisfje\nvXtSqRRNJiUnJ7e9V1Gdtb8ybaN2uuerjT+M4hNjtL+aMD8A9O7dGwCUSpaf4urVq1Uq1bZt21q+\nEjU9evTA2zhsudVB/3HIoac2yCZtT8mRHlOiKSVVUZVsZqCu0uLj4xMSEsxVV8fGa/rSbMnUhwmL\neizcAKCOTKHx/icUglQKJnXrJR7qfa+wSn45J/TpziK/Lpq7KQCZWtoQCZCs7jMRrIu1xwwtARo2\nrcr8qeBXquLvrzX2IiE4AFAUZXThmPryLNaPRgbz5adpuqCgQCAQ9OnTp6GhgZleW1vbuXPnkSNH\ntvLSUGcoNjYWp0RFRbm4uLTycPPh7+9fk5t5d/6wu/OH1eRm6slp0JQSx4fX9cPlypec3Ht3/rDy\nG2cbv+OZJI2PqWeVlAWVos1X9D13qXoyyZifvk3C5XZCO8IcEqa971TXgA+qs5Kqs/Yz0yMiIrDo\nru1CcL6bD+tHI4P58gOAp6fnvHnzMjIyvv76a2b6V199VVxc/OKLL7bxGrmAoJuvT8x+1/4jsyVT\n9WQjinAugJyu5iYsBgCQy4H1V0ZREBZm2vkkHKJCZ9gk4sGBa1jbIloC5kuBdg+Jbi66Exu4kpyb\nbxxKpdLb2xsA5s6du3v37t9++23+/Pk8Hq9Pnz4VFRU42//+97+9e/deuHCBtRAu95DQhv7uEUbD\noYOuxfzcfJSthFOeGrRpelLYZQPrp22SV1ZaUFoqHcWDg014anA4g6QLo4XgnH3ADx8+fOWVV1xc\nXNBF8Xi8qVOnZmU1De5FREQIBIIBAwa0a9du/PjxtbW1GiUUFxcDwOeff45ToqOj3d3dLXQBumG9\n520fvuPso2wNNlN5mYymKBZTRFE0RZnDILWMkjFwl2yF81sSjrcTxzVIRcdDNFKwCgAJ8NpSOHeo\nra3966+/rl69Wl5ezkw/fvw4AJw5c4am6ZSUFCcnp3379lmpjgajfc/Rkpe784fpPzD5n0JqzVls\nk5L/KcS7pEfuer2yWKcnNM7D8XaIyYn/gH0OyZwrkxAaT7wZMoZNMm8trAzH24kDzSExQTrp8qvL\nmIlYCK5SqWJiYuzDI7izs/OgQYOCgoLc3NyY6deuXRs4cGBISAgAPPvss97e3qyqPFsBLXkRfnNR\nfzaRXxemIjxyz200paQqrJJfzinwf0V+OcdhXeFZgIqb50oV+yrKH4BaSdSESATmDOisKqyiurjo\njHcuJh4cOIGDGiS+m4/HqESmBBzB9L4aGRlpx95X33///bNnz6Lts2fP3r9/f/DgwdatUhsRdPPF\n28oFw2vzslizaTsZCtuSGvZNKrZDwthzRPhgJtz6j3LtP9Kt/yiQSECpbGaBzPz+hwQOypWjdOYg\nAgcO4KAGCQA0lGkYFEIJ7N37art27Tp27AgAiYmJL7300pw5c8aNG2ftSpkGZIqyJVN1LZ7V9hGO\nrRHaQKuXLFJZh6MppCxakCSVglgMYMaQshjUM9a9m3hwsD6Oa5AwxSfG1OZfYKYwheB26X0VkZ+f\nP2nSpHfeeWf16tXbt2+3dnVMBlKEe4RNL9gXp8ehA9MmaUB5uhCBuLmpuHkOxGKQSEAiaewqKRTm\n7icheEtPEg8O3IQYJGjvO6X82jKm9x00mYREd3K53M483SEqKytDQ0OLi4tv3bq1aNEiQ12AcxxB\nN1+v6Ut9YvYX7IvTM3ynC1VhFekhmZUsyZSmdwXUVQK1gzvzIw0Xyi/nKO4UseyjSIgKa0IMErT3\nncp39Sk9N0vDJtmx91UA+Pbbb+/fv//tt9/W19erVCqVSlVRUWHtSpkYt/6jhFsugu7hu16eLqzD\nOJSOdIKp8Jq+tJnTVbG40cGdRTpJkvFCkV+XyD23SYgKrkEMEvDdfDoErwfQ5xHchN5XOcKZM2dK\nSkr69esnVPPjjz9au1KmBw/fsXq9Ew/1Tl7ALuVIXjBYZ+xRQptx6z9K0+mq+cP3MZGEC4F4cOAe\nxCABqEV3DRXZGkJwkUiEheB2Jrr7+eefNVYAzJ8/39qVMgto+A5/1Ri+ozxdtGeSJOFC0kMyN+ih\nPExY1PidoprUDeYfkEBiSyT9Z9tNBA7WgRikRvhuPh1HJVZn7a9MaxbhmykEDwsLsyeb5IAoFwzX\nHr5j+rujPF3ouLEtRMImmAL0olB583xTSFns7dsMASm0QSEq5Ck5+sKMzdNTAAAgAElEQVQmNdaH\nCBwshKMYpPj4+BbzCJ4Y4R68Xjt4REREhFgsBnsXgjsCuobvDu76vurkf7zSD0l06O5sgtY0ck7R\nzOkqaIXvMz/iod7ScKHOsVkRYzLJ9gUO8fHxAQEB1q5FS1jFP4SFabu3DKVSiYTgoOV9leOuOOwS\nU91zDd93Nv0obbTyNbmZaVO8m74rlbRI1OhMKDnZatVigkNUiKxdE1PA8XbiKD0kI3A0IbijwTp8\nR7Awgm6+/vsfNH3HEnCwkLoBI4w9x74DCxwUZDLJ7BCDxE7p2Vl6RHd2KQR3NFqzeJZgBXCMc5UK\n5HLLnBOtPNMncEBIAWIYH4KpcYgQ5kbQIXi9hkECdT8J+W6Qy+WhoaEikWjYsGE2MDJrXwwbNqzt\nhWD1XcG+uNLkfT4x+1s8hGA+0qf29InZ79Z/FACATAZCIQBATEyj9M7MUJ4uye8Fs0Q6b9wNkKxe\nkyRXTyZRAKYMuU4AADKHZDjMkOdKMzvMJ1gAHA19SrCftetiPByfG2gRzeghOI6fgQEzzQieTLLl\nqOccbydkyK5lNITgDuJ91XFAi2e9pi+9Xu5k7bo4LprRQyIiLOzgDiOMPcfuwUECILZkRRwRYpBa\noDJtQ3VWUnVWs/EcpvdVYpPsAEE3X4+w6dauhUPDjB4CYAUHdwgUNonFg4McQAggb54oVH/IfJKJ\nIAapBVwDFrX3nVKZtpHpEZwpulMoFHbsEZxAsDBZkimNW5Z1cIdAYZMAQFPgcE9rHZKK8SGYCGKQ\nWgZ5X9X2CJ6cnEyE4ASCCam4ea6Z01XLOrhDsHtw6AVAqT/NcmulENoAMUgt00rvq3JLSVQJBHtF\n0+mqZR3cYUR+XTRDVIgBlOoP1Ty3ksjtTIZZDBJN0xkZGQUFBeYo3Cog76sAoOF9FY3dAYBKpYqJ\nibEzj+AEPdhfI+cIXtOX1j7KanK6alkHdxjJeKH4WW+dISowKhKiwpSYxSDxeLzIyMivvvrKHIVb\nC2STNNQN0Nz7qp15BCfowS4bORcQdPPtEbWhyemqxR3cYSKGerMLHDAUABAPDqbEXEN2zz333KlT\np0pKSsxUvlXgu/l4vsriGJgIwR0Tu2zkXEDT6Sr23SCXW1ICjgQOypWjNHdIAKQAMka8c6mWAI9g\nFDyaps1R7tmzZ2NiYmpqaiZPnvzkk08KBAKU/uKLL7Zv394cZ9RDQEBAWlqaacuszb8geGIE/oq6\nR2jITiwWy/BkLMF2MLSd2H0jtyK1eVnK94b3iNrQKMdXKAC96lEUKNmiRVgLuTqCHwWQbAMCB463\nE3MZpJdeeunu3bva6efOnfPy8jLHGfVg8meAFid5jErku/ngRGbAJKlUKpGQiU4bw9B2Yt+N3OoU\n7ItrFigkLKyxeySTWcafEBPe0pOymYHsgbJi1FEqKAAu2UpWuN5OzOQBoqSkpKCggKbp3NxclUpF\n03RBQUFBQUF9fb2ZzqgHk3vLqC/PKvlzpna6kvHuJpVKTXtSgrkxtJ3YdyPnHEplozMhygpOe6RH\n7lJrzurcLVL7E+KMnyNdcLydmGsOycPDIykpafDgwWPGjAkPDw8MDPzyyy/btWvH55v4jDRNx8XF\nhYWFjR079rvvvjNt4brgu/l4jE7UTtcQghPRnX1jsUZOAACgKEBuJFUqC0emAICIod4sk0kYEu/c\nVJjJ0O3atcvf3z8yMvKnn346cODAJ598EhgYuGjRIpOf6OjRoy+88EJmZmZKSkpgYOD//vc/7TwW\nfinAE0jE+6ptYWg7sVgjbw3+/v6bNm2yyqnNSjOnq0olTVGNnSSOhO/DKBl+V2XWrgwbmzZt8vf3\n53gPyVwGacKECQsXLmSmbN++3d/fv7S01LQnOnDgwC+//ELTdF1d3XPPPXfx4kXtPOZ7BjWPzhf8\nSlX8/bVGOvEIbosY2k4s1shbA8f/aIxGM6SsTNY4cCeyTgBXWPKH9Mhd9n0yhiNwpSUrZQAcbyfm\nWhirVCrDw8OZiePHjwcA1kngtjBx4sRJkyYlJiZOmTLF399/yJAhpi1fP4InRrgGfFCZtlHDI3hE\nRIRYLAYiBLdfLNnIHRnNkLJMB3fW8I0imxkoPaaUp+Sw7BOr1Q0qslrWSMy1MNbb2/v69evMxBs3\nbgBAz5499R+blZV16dIlZkpGRsaRI0euXr3a0NCAUg4fPrxkyZIlS5Zs2NBoBoKCgmbOnHnr1q0/\n//zTZJfROlwDFrkGfFCdlaThfVUikWCP4MT7qv3RlkZOaBN4TYU1HEiKh3pLw4Uxx5RNXoWY4Hjn\nKrUcnGAI5ooYGx4eLpPJ3N3dX3755Xbt2l2+fHn9+vWDBg3q2rWrnqPq6+tXr17N5/NxSND169dv\n27ZNKBRmZ2cHBQXJZDInJyehUBgaGgoAXl5eSUlJFEUNGTIkMDDwwYMHR48eRbssSXvfqbX5F8uv\nLWMKwZFXISQEl8vlyERZuGIEs2JcIycYR1NIWeTgDnkSiowEi6/5ixjqrbhTFLnnNovMgQKQAYQB\nqADkJKqs4ZhpKLC6ujoqKsqfwcSJE+/du6fnkOXLl4tEIn9//3feeQelKJXKgICA/fv30zSdnp7e\nr1+/n3/+WeOo2NjYuXPnlpWVVVZWzpkzZ+PGjdolW2DYFAnBi46HaKQTIbgNYWg7MaKRmw+Ozw20\nnZz4D5qpG7AE3BpztMqCSmrNWdHmKzp2MyaTki1Zr5bheDsxy8JYmqb/+ecfT0/PvLy827dvV1dX\nC4XCYcOG6ZfD7t27t7a29vjx4y4uLkjAvXfv3i+++CIlJQUd+Oabb3bt2nXdunXMo/Lz86OiotLS\n0gQCwaBBgzZt2uTu7q5RckBAANpYuHBhdHS0KS+VQUNFdum5WQKvEe7B65npcrkcDdmhPhMaxyNw\nhPj4+ISEBPy19WsGjWvk5oPrCx7bDPLd4CGa3mPhBgAAubxR/C0SQXKy/mPNgaqwShh7ThoulIwX\nsuyWc9SDA9fbiZkM3ejRoz/++GMjDly7di3uIW3cuHHixIl4l0QiEYvZF56VlJSUl5frKtNiLwX1\n5Vms6UR0ZxMY2k6MbuTmgONvviah5OTeu/OHld84S9M0rVTSIlFjP8lKEnDZpQf6dksZ/STOwPF2\nwmnnqg0NDU5OTvirs7NzXV0da04PDw83N7e2nMskMD0JMSHeV+0S4lzVwiCnq43RknCMc7Bo+D4m\n7J6EMETgYDjmMkgTJkxwc3ObNGnSxo0b9+/f/6ua6urq1hciEAiqqpqCkVRUVLRr184MlTU9xSfG\nMEV3ABAREYFFd8Qm2QcmaeQEg0CRKRpDyopETeH7rBoeUxh7jiVsEkU8OBiMuVR2a9asuXfvHgBs\n2bKFmR4SEtJ6R8g9e/bMzMysrKx0dXUFAKRrMK4+8fHx5ps90qa975Tya8s6jzuDU5iiO4VCERkZ\nSTyCcweNmaRWYpJGTjAIQTdfr+lLC/bFufYfKejmCxJJoymKiQGRCCjK8lVCpihyz63k9wZr7qMA\nkgHQHJMcIFTdZyLowhzjgA0NDY8ePaquri7QokW/k8w5pLy8vIEDB0okkkePHiUmJvr7+ycbNVhs\n+WFTXZNJSqWSUv9miOiOaxjUTtrSyM0Bx+cGTEhNbmaz79h3g44JZgugLKjUt1vGIQ8OHG8n5loY\n+9prr8XExHhq0aIGicfj4e2uXbvGxsYeOnRo9OjRq1evfvvtt21FoqZrMknD+6rcquMMhLbQlkZO\naAuCbr7NvuOOkUJhyfB9TChPF327xcSDQ6sxk6H76KOPRo8eXVxc3Pai6uvrc3JyampqjC7Bii8F\nBb9Sj1M/1Ehkel81rs9HMAeGthMTNvK2w/E3X3PQtCwpOdm6Du4w1Jqzyf8UsuxQciVEBcfbCadF\nDQg+n9+jRw8cjtM44uPj23K40XQed6Y6a7+GpzuxWIxFd5GRkSimH8GKxMfH48VqrYeIGqxIbV5W\n7aOsRsUdjnFuJQd3CFVhFdXFJXLPbSJwMBoSMdbsVGftL7+6zDXgA9eARcz0mJgYZJbQ4iTrVI7A\ngESMtS1Kk/c1BjgHAJUKhEIAK8c4VxVWhX2TCgDswZNUaoEDBSCzjsCB4+3EXAaptLSUdc1Q586d\nLT/CbvVngEKeuwetFzwxAiei7hEK4icWi4nozuoY2k5II+cWMTGNEfzEYss7uMMgDw7iod6ymYEs\nu+VW9uDA8XZixoix2pO9Djvf2953qsBrRPm1ZQ0V2TgRCcGR6E4ul8dYw3UxoS2QRs4RKm6eAwCI\niLC6ugEAKE8X2cxAeUpOzFG2jpqYCBz0YeJfjlQq3bFjB9ouLS09cuRIWVkZ+nr9+vXp06eXlpaa\n9oytxFpzSAi+m49rwAd8V5/Sc7OY6UzRnVQqJTbJWhg0h8TZRu6YPExYlJuwGIDhu0GlskpkCgwK\nUSG/nENCVBiKiQ3S//73PzxFn52d/cEHHzx40Bhcq6io6K+//qqtrTXtGVuJJVfFssJ38+kQvJ65\nVBahIQRXWO/NzpGJjo5u/TgGZxu5Y+I1fWnto6yHCYsAmqsbrPpTihjqjQQOLPsoInDQCRlbsBy6\nFieJRCI0gUREdwSCoQi6+SJ/QhU3z3HBwR2C8nRJfm8wu7QB1BNICDmAwiJ1sgWIQbIChQeEeoTg\nyL1QjBrrVJFAsB1c+49scrrKdHDH5Z8PBYCEFyqASACVNevCHYhBsgIo5LlGYkREhFgsBrVNksvl\nUqmUuHIgEFoEd5Iana7iThKKKmtteEtPEoFDKyEGyQq4BixinUySSCTYIzgZuCNgaJqOi4sLCwsb\nO3Ysil1J0AA7XQUAoKhG2Tc3OklI4MC+jwgcmmN6b99Hjhy5desWAFRUVADA8uXLka9u60qPLOzt\n2ziYHsGtXRfHwlBv3xZu5MePHz969OiPP/6Ym5s7b968UaNGDRw40Bwnsmk8RNMbe0igVjcgxw0R\nEWBVH5iS8TqiyoJ64C4MQAUgB6AAJOwZHQQT95AoiurSpUtZWVlZWVl9fX2fPn3q6urQVx6P16dP\nH2dncwW80A83rVHxiTHFJ8bgr3K5XNsaCdWQ+STzYZDKzvKNvLq6OioqytfXNzg4uGvXrpWVlaYt\n3z4QdPMVfnOx8Qtn1A0tQxGBQxMm/uV89dVXpi3QvvEYlVh6blb51WXuwesB4N69exrWiHSVOIjl\nG/nEiRMBIDExce/evf7+/kOGDLFwBWwS3ElC4fuQ0sGq8JaeZPfgQAHI1NKGSOt4cOAIZA7JmvDd\nfDxGJWLvq7169aLUMLNppxBsmqysrEuXLjFTMjIyjhw5cvXq1YaGBpRy+PDhJUuWLFmyZMOGRkFm\nUFDQzJkzb9269eeff1q6xjZF+tSejZNJ2IEQN0YXiAeHFrHOABoBw3fzcQ9eX351GQCIxYvE6vc4\noVDI7B4R76t2Q319/erVq/l8/rBhw1DK+vXrt23bJhQKs7Ozg4KCZDKZk5OTUCgMDQ0FAC8vr6Sk\nJIqihgwZEhgY+ODBg6NHj6JdBFa8pi8tTd7nNX0pUBRIpSCVgkoFkZFWdHCHEA/1vldYJb+cE/p0\nZ5FfF83dEQAKAIW6n+SQvi1JD8n6tPedioTgtfkXWDMgIbiFa0UwBytWrBg3btzp06dxikql2rp1\n65o1a37//fekpKQrV64cOHAAAPr27Ttp0qRJkyaFhISkpaVt3Ljx8ePHVVVVV69e7dGjh/WuwAbw\nEE1vmkzihoM7jGS8UOTXhYSo0IWjGCTr+rJrEdeARe19p2h4X0WgwTqFQhHJ8blZW8a4eEhGEBwc\n/NZbb40Y0eT0/eLFi+7u7pMnTwaAPn36DB8+/MIFzfeSd955p7q6OiQkZMyYMe3atXvrrbdYCw8I\nCAgICOB4U7cAzULKcsbBHUYSLqS6uKAoFZpQZhE4oOaNME2J5sPKAQItAseDJCLqy7NK/pyJv8pk\nMqlUKpPJlEolnkCSSqVWrKHdY7F2snbt2nfeeQdtb9y4ceLEiXiXRCIRi9lDipaUlJSXl+sq0yYa\nuYVpCikrEjWGlOVGgGZlQSUs+UOceIt9t0wdW5aiaaWJT83xdkLmkLgC383HY3Qi/ipmiIKSk5OF\nQiEAyOXyXr16iTmgFyKYioaGBicnJ/zV2dmZNcYSAHh4eFiqUvYACin7MGFRj4UbQCZrDN8XGWnF\n8H0YytMl+b1glmkkhBjgHoBULXCwfn0tBzFIXAQLwRFowSzyuxoTE0NRlMiqC/0IJkQgEFRVNU0n\nVFRUtGvXzor1wcydO1dDCmiDdITrhyH+MACAv39jGveHrRD+AADDKobtiNzhOAIHYpA4R23+heqs\n/Xy3J5khz8Vi8b1796RSKfIInpycTITg9kHPnj0zMzMrKyuRr4f09PR+/fpZu1IAAJcuXeJyaFEH\nISAgwKE8ODiKqMGGEDwxwj14PdMaISQSCdMjuBVqRjADISEhTk5O69aty8/P37Nnz/Xr18eOHWtc\nUUTOYLfITSBwsJhypy0Qg8RF2vtOZU2PiIjA3leJ6M524fF4eLtr166xsbGHDh0aPXr06tWr3377\nbaPHY7npH4tgAlQmCFFhkH8sa0GG7DhN8YkxHqMScWQ/pvdVuVyOHIRbt4YEI1i+fDnz68SJEydM\nmJCXl+fl5SUQCKxVKwJHkaoFDpEMUbid4ig9JFsczWioyOa7+pSem8VMZIY8l0qlxOOqSbD6aAaf\nz+/RowexRi1SVlaGI8Qzt20OAy4Eh6hQ2P9qWUcxSLY4msF38+kQvB4ASs/qtElyuVzBgfXnto5N\njGYQAGDw4ME//PCD9rbNYcCFUAwPDlI7t0mOYpBsFOR9ta7gAnJ2hxGJRDKZDNSTScQpOAFscxjA\nUGia1t7u168fX02HDh2eeeaZuXPn/v333yY5o5kKZ70QnVAM13ZyIwUOVh8GaA3EIHEd5H0VewTH\niMVipuiO2CSCLQ4DmISGhgZPT8+1a9euXbt28eLFfn5+SUlJgwYNksvlHC/cAEQMd+BGCRxsYhiA\niBpsgPa+UxsqsquzkvhuPkwBXkREBFI3IJtEPIITHJbOnTszpSI3btwYP378okWLXnrppe7du3O5\ncAOQqAPLquxW4EB6SLYB8r6qIQdHKjsiBCcQNBgwYMCKFStKSkp27dpVWlo6ZMiQbdu24b3r1q0b\nNWoUNwtvAYmdCxyIQbIZtJfKgloIjrw2yOVyIrojcI4Y9ceyvPbaawCQkZFRX1+fmpr68OFDvCsr\nK+vq1aucLVwfFGMySQogN9d5rAUxSDYPEYITEBwVNcit89fp7e3N4/HMNI5t1sJbgGIM1sUYIHAg\nogaC6WmoyC4+MUZDdIf6SWibCMEdFocVNbBSW1tL07RBLtLv3r37BYOzZ8+asHBTImoucGgdRNRA\nMD1ICI59N2CI91UCgQnSnfbq1av1h9y+fZspXli5cuXo0aNNVbjRxBxVSsYLNVOZAocw+xE4OIpB\nio+Pt5v3R21rhEBuhJBNIqI7g4iPj09ISLB2LbiN3Nh5IJV6Q+tPtVWIjXR0nZiYCAADBw7U3lVS\nUsJ6SHh4eEFBAf6K/K+bqnCjkR5jM0igtkkKtcDBLpyIOYpBshtrpEFt/gXBE03xsCMiIhQKhUKh\nQDYJzy0R9BMdHR0dHc39EXZrcq9tzj3bcqzhnDlzJi4u7qmnnpo5cyZadopHq2pqak6fPs16lEAg\n8PT0NFPhRkPH6fD+TgHI1GZeCtALQGzaM1sBRzFIdkll2obqrCRd3lcVCkVkZCSeWyIQ2kQvtfca\nQ1GpN4w7vHUUFBR8/vnnAFBbW3vlypWDBw+6u7tv3rwZRTsMCAj4+eefg4OD/f394+PjMzMzXVxc\n8LHx8fHjxo0LDAw0eeH3799PSkqKjo5m+nc3JRSATD2NFANAqUXhtov1oqdbDo6HkTea+vKskj9n\nFh0PqS/PYqYrlUo8gSSVSq1VPZvDptuJyStvsgIpmgaapkxTmJ+f35YtWzS2mbbE3d19yJAhyJ8W\nPurEiRNdu3YFAB6PJxKJlixZ4u7ujnbV19cDgEwm03XGthR+6tQpAKirq2vlhWiDnwK15qw48RZ7\nFaU0Da29yRxv5KSHZMMg76ul52aVnpvVedwZnI6E4EKhEADkcnmvXr3EYrHVakmwFPY0UWoQt27d\n0p/h+eefz8nJuXPnTvfu3Tt1+v/27jysiWttAPghIaxWK1Rl1QRrIqAWRHEpCrhbvXq9YClqIVQf\na7VUamu1rZaApVat1QLfrfRWiEuBqnitWu2tXqGtuHKlLW5Aa4KEgsiiKAEJSb4/joxjEsKWMDOZ\n9/f49JmcTIYTcuibOfPOe/ohhLZv306Hg3de7hujBUnn+P3tOkhwiEHtrXfOiAulkPbNbDjpTqNU\ntJcILpfLExISIBGcDdgZjTqJy+UKhUIcMHr54Bs2bHBycnJ0dIyKimptbe3ej+A72WW84i35USa9\nXGng6fi2GVFpu7knjEj7hoDEeBwHj2cmZhmvvgoVwQFl4hGSWEgOWPecP3/+5MmTqamp+/bt++67\n77p9HPFYV8kMQcKPsrw/63Wf45MyvyUMruAAAckS8J4bby9a3VT8hU57fHw8uSI4BT0DQIxQvMkS\nwDZt2jR58mT9bTr76quvxo0bFxMTM2LEiFu3buHG7r2R6LGu/P52Mdk3DDzHJ03WJfR2WqOpQECy\nEPaiOKd5Bm48io6OhuqrwGJERkb6+vrqb9OZl5cX3nB0dMQ5FKi7b4TvZJfxig9CKPSfVww8LSZV\ncGDm908ISBZIo1QQ21B9FQBqmTbnm+9kl/vG6NyVow0/Tax3Lu9CVSH6gIBkaRryIxvOtbvkOVRf\nBYDp+E527T9HWu9cyrwlKiAgWZo+/tv0G8kxCaqvAqCDwzHL/wk5HI6VlZW57opFSJB0roMEB2k3\n1zunCgQkS8Nx8CDfk0QICQmBpDvLRtPlJ+iNw+FotdqoqChzHDwoKEij0RDR7sKFC+vXrzfVweV1\nzR0nOMifrHcOy08Aiukkgusk3UFMsjBwHxKr4AQH2YftrE4r1k1wgPuQaISFXx5xpTtVzQVyIznp\nDhLBCYz48giADmMXk5ChBIcE9Gbtm3S+sMSWgMTCL4/2ojhbz7DGX9fqJ91BIrgORnx5BKA9Vu+c\nSfiP3l0ffL0EBymKrY2l822zbAlI7GTrGc6x92g4FwmJ4ABYMMkMgbSgsuMEB3kv9qlbICBZMlx9\nFSEEieAAWDCigoO8rln3OT4pwYH2ICBZuA6rryJIBAdAT1FR0YEDBy5evGjw2fLy8kskSqWyl7un\n40kFhy/1KjhIDd2NJGj7R7PvohCQLB9OBIfqqwB0klgsDggIwCXmZs2apV+i+/33358yZcrcNnT4\n28EVHOR1zbqJ4PpL/cpJ/2gGAhIrcBw8nObJ7EVxOu1QfRUAHadPn96zZ8+ZM2eKiory8/NPnz79\n73//W2ef33//PS0trbqNj48PJV3VgZeokF6ufCrBAS/1y396xV79FnqAgMR2kAgOANmvv/46cuTI\noKAghNCYMWNcXV1lsqcS2FQq1c2bN4cPH37jxo36er08AkrhJSqkBaQ1k8QIydr+8RFCCPFJLTRb\nFgQCEuvcOz2pvaS7vLw8SHBgLhbebGcOb731Vn5+Pt7Oz8+vqKgYPfqpSqY3b95UqVSzZs0aNWqU\ns7Pz66+/rtVqqeipYfEzBQbvlk1JSamoqOj9/nQJBCR20SgVOBGc3IiT7nBMgqQ75mLVzXYajaak\npKSgoKCurs60R7axsXnmmWcQQllZWbNnz16yZMm0adPIO9TV1YWEhBw9evTRo0fZ2dlff/31vn37\nTNsHc4iNjXV3d6e6Fx3RsoBQKKS6CwxAzEvg+ER1dyjA6HFi8s7T9rfR0NCwZMmSPn36EP8TmzFj\nRlFRUeePUFdXZ2Vl9cknn7S3w927d+fNm9enT58dO3ZoNBrjR5s+ffprr73W+Z/eJT35FNCa/4qz\nrj/VlKFNdk7WZvSwU2YEZ0jgMSIRHCfdQSI4oKGampqAgID9+/cvXLgwOzs7MzNz8eLFubm5U6dO\n7VKqG/7fn8GnmpqagoOD7927d/369bi4OP1a3fv27du+fTvxsLW1tb1DUQsnODzVJEapzqmmWr3X\nHCAgsVfdUQEkggNm2bx5c2lpaWpqanp6ekRERGRk5P79+999993q6uqdO3d2/PpO2LVrV0VFxa5d\nu9RqtVwul8vl+DajVatWZWZmIoS0Wu2HH354/PjxR48eZWVl5eXlzZ8/3yQ/2rTEY12126dQ3Ysu\novL0rLfQdvKBWsqbO+pPBTXfPqjTjmMSQojP51PSMaowepywYcquoaHBzs7O19dXp/3hw4cLFy6M\ni4vr5HHwZae33347IiKiT58+Dg4O8+bNq6qqws8uWLBA53+SX375pVarRQitWLFCq9VqNJrVq1fz\neDyE0DPPPLNlyxbTvUVdpvoUZLVNpj2gmUBAYjUck1runic3ymQynAiOEBKLxVT1rfcxepywISAV\nFBQghBITE3t4HCIPYujQoWvXrp0yZQpCaNGiRV06SHNzc3l5eYdXmHrIJJ8C/+N8/sf5Jjyg+cCU\nHavh6qsGK4JD9VVAN6WlpQghPDJ7ztXV9cqVK1u3bv3vf/87YsSIn376qUsvt7W19fDwMN9qsCZk\nuIIDLVlT3QFAJVx9teFcZMO5SPI6szjRTiAQIITwDF58PM3uoAO9y0DVToQQaUkevIPOQxPujxDS\naDQIIf1CPt0THh7et29fvD1p0iSpVGqSw9IQ38kud6V/6D8L+f2Nrp9EAxCQ2A5XX204F9lYuNbR\nfxvRjs+T8IJJUqk0ODiYmMcDLLTncqXkR70VdxAiLpsLks7pPzTh/gghLy8vhJBO3QQsMTFRLpen\np6d3/E7auLi4ENvEKuOWKmRof1zBodVZSHVfjLGcgJScnKxQKKKLH0AAACAASURBVLZu3Up1R5gH\nxySOg4dOu1gsLisrk0gkOOmOuHkWsFD0WNfosa5GdtCpDtDu0trd3R8hJBQKeTxednZ2QkICea6s\ntbV1x44d3t7eHR7BCC0tU7dNKH6mYIiT3ea9JVR3xBgLCUiFhYXp6emTJ0+muiNMpR+NMDxTh2NS\naGiowS+ngA06WC1bbweT748QcnJyioqK2r17944dO9asWUO0f/755/fu3Zs1a1aHR2A58VjXzVT3\nwThLOFFtbGz86KOPVq5cSXVHLMG905NUNRfILeTqq/iqEqAnNtSy27Bhg6ur6zvvvBMVFZWVlXXi\nxIk33nhj/fr1w4YNW7v2qRW/bt261dU8BcuWkpIiEomo7kUHLCEgJSUlRUZGDh48mOqOWAJbz7DG\nXw0s5UfEJHxVCdAQG2rZ8fn8wsLCuXPnHjx4cNGiRXPmzElLSwsLCztz5oy9vT2xW2tr65tvvrlt\n2zaDB8FXjLhcLrmF/NAixcbGFhcXU92LDtBuyq68vLyysjIwMJBoKS0t/fPPPwcNGvTCCy/gkXTy\n5MlTp04hhAYPHuzr61tZWZmUlPSf//yHsk5bEFvPcP1lk3BMCg0NlcvlUqmUz+dD0h2gyqBBg44d\nO9ba2nr9+nWNRiMUCh0cHMg7iMXivLy8srKyOXPmGDxCv379dK4YJScnJycnm7HToHPoFZDUanVi\nYiKHwyEC0rZt29LT0wUCgUKh8PPzy8jI4HK5AoEgODgYIeTs7JyWlqZQKMLCwhoaGu7fv79p06aN\nGzdS+iaYrb2LSZAIDmjF2tp61KhRBp+aOHHimDFj9FfVA/RHo4C0fv36ixcv/vXXX0R6sVwu3717\nd1JSUlhYWGlp6d///vejR48uWLBg+PDhw4cPx/t4eXnhSlM///zz2bNnly5dSlX/LUzdUYGtZzgk\nggPGWb58OUJIJpPRf4YK6KDRNSR/f/+lS5eOHz+eaLl48aKjoyMuLTVs2LBx48ZduHBB51Vubm7P\nP//8888/7+7u3qdPHzc3N4MHF4lEIpGIDVd9TeWZiVmPyg9ZfPVVfKUXo7ovALAdjc6QIiIiEEIK\nhYLILb5z5467uztxz9rgwYPLysrae/nMmTNnzpzZ3rPwXamreM+Nd/Tf1li4FiFEvqpkYYngsbGx\nRC4AxCQAqEWjMyR9Go2GnPpibW1tqqohoDNsPcPtRasflecYSQSHpDsAgKnQOiDxeLzm5icVrpRK\npY2NTfcOBZN13WPrGc5zHm/x1VcZcYsGABaP1gHJzc3t9u3bTU1N+GFJSUm314Rnwy0a5sBx8LAX\nrebYezSciyS346Q7vC2RSJgekxhxiwboEkbU4QY6aB2QgoKCuFzuli1bampqsrOzi4qK8MoloDfh\niuD67Xw+n7iAJJVKYclzQCufffbZ8ePHqe4F6BoaJTVg5O81AwYMSEpKSkhIyMrK4nK5y5Ytgzxj\nSnAcPMiLUxCIRHB8MSkjI4Mo1gJ3KQEAuozqFQI7plarKysrW1paun0EoVCYnJxswi6xmfLmDp0W\n8pLn+MIS49Y+T05OFgqFNF9M0zg2rBjLQmz7WGk9ZYdxOBwXFxe8gn23wTUkk2gq3vmoPOdR+SFy\nY3x8vFgsRgjJ5XKG3pkE15AAoAPaTdkBOsM3JNl6huu0x8fHy+VyuIwEAOgJBpwhAVrRL70qlUpD\nQ0N1opGgDdMT8AAAvQbOkEA33Ts9CWc6lJWV6czUMXTiDtDfgwcP7Ozs8AQ+eZttfbBUbDlDghtj\nTQvfJ4sLCw0ZMoTfhryPfgttwY2xTDF69Oivv/5af5ttfbBUbAlIkNRgWhwHj75t1VfFYrGsjU4E\nys3NZUT+t2UkNbDhW5eWtI6R9uk1jVjVh25gxLcutgQkYHIcBw9H/21NxV/oVAQn4OqrvdwrNoNv\nXcAIRnzrgoAEuq+96qsIIaL6KsQkAEAnQUACPWIvirP1DCOqr8bHx0skkoyMDKL6al5eHlQEB+bT\n0NAQEBCQnp5OtGzZsmXixInmeyEwH7Zk2aWkpMCEhpnYeoarai7itc/xHbJYbm5uaGioXC6XSqV8\nPp/OF5NSUlJSU1Op7oWFIvL+zTMA1Gr1lStXqqqqiJby8vLCwkLzvRCYD1vOkCAamQ/HwaPvi1n6\n7eSK4FKpVCqV9mq3uoIR0+uMJJcjqRRJJEgqRXAzAOgIW86QQO9oLFzrSCoNTq6+mpCQwOfzoTwu\ni8TEoLy8J3FIIEASiZnOkzp069atQ4eelLx68cUXfXx8KOkJMAICEjAZVc2FR+WHOA7u5GoOYrG4\nrKwML3keExOTm5vLlJuTQI/gcyPyQ4SQRIKioxEVA+DGjRvr1q0jHn744YcQkGgIAhIwGd5z4+1F\nq/VrC+GrRzgmhYaGEqsoASaRSlHPq0Dx+airWZdicVdPqu7fv6/fOGPGjNraWuKhvb09eTVqIy8E\nvQkCEjAl/WiERUdH5+Xl5eXlESsn9XLHQE+VlZngIpAZLiM5ODgghIhLgC0tLT///LP+bjwez8nJ\nidzC4XA680LQmyAgAbO4d3pS34lZOPUOtV1MYkrSHTBgyJAuT7Xphx8zTNbZ2tqKRKLDhw/7+/sL\nhcKUlJTbt2/b2dnhZ1NSUqZNm+bt7d3VF1ZUVOTk5MTGxsJS6L2K2uWYegcs0NfL1I3l98++Un8q\nSKedPFknkUgo6ZtBsECf6Q8ok2kR0v3H52tlsp4cdejQof/85z91tk+fPj1gwACEkJWVVUhIyJo1\naxwdHbVarVqtRghlZGS0d7T2XqjVavHax62trZ3sg5nQ7mM1M0j7BqbHcfDo478NtVVfJegkgtNn\n/SRI+zY9Ph+1LSX8RHy8OU6Spk6dWllZWVxcXF9fn5ubu3379ocPH5r1hcBM2BKQQC8jV18lt4eE\nhOAlz/HFJFiowpLFxyOZ7HEE4vORVotI902bFpfLFQqF/fr1M+0LN2zY4OTk5OjoGBUV1dra2uNu\ngg7ANSRgLrj6Kj5JIic7QNIdi/D5KD4elZWhIUOo7kp3nD9//uTJk9evX3/ttdfmz58fFhZmZOe7\nd+9u2rSpqqpq4sSJb731Fk6a+Oqrr3AkW7hwIZ4eBMZQPWfYG2g+bWrZlDd31J8Karl7ntwok8mI\nO2T5fD5VfdPB6HHCkosNmZmZV69e1d82qMNrSEbga0jFxcX44YgRI7Zu3Wq8DxKJpLGxUaVSRUVF\nTZ48uampafXq1UVFRfjZL7/8shvdYMnHSoApO2BeRPVVciNOuiMqgkP1VdBJkZGRvr6++ttm4uXl\nhTccHR1xeGuvD7///ntERISDg4O1tfWePXusra1HjRoVERExYsQIvGdISMjNmzfN2lsLAAEJmJ2t\nZzhe7JwMxyRctUEqlSb0/KZLAEyt8znff/311+DBg4mHaWlppaWlRUVFRMuAAQMqKytN3D+LAwEJ\nmB1xN5IOBlVfBcC4adOmHTt2jHi4ZcuWkydPvvvuu3jqDyF05MiRSZMmUdQ7xmBLQGLD6s70V3dU\noJ8Ijqs24OqrVCWCM2J1Z9A9OLmgG6+ysrLq/BmStbX1wIED9+zZc/Dgwddff/3999+fNWvWqVOn\nYmNjY2Jili5dOmjQIGtrSCLrgJWWOWvCd5tIJIK7TOhAo1TcOz3JaZ5uWl1CQgLOBcfnTFRVX2X0\nODF55xn926CKRqNpaWkhyj1gSqXSzs6ue3GRbR8rW86QAB1wHDz0oxFqW2cWwZLngOE4HI5ONEII\nOTg4dC8asRD8mgA1VDUXyA+jo6Mh6Q4AloOABCjQWLi28de1GqWCaIGku85ITk5+7733qO4FAOYC\nAQlQwF60mmPv0XAuktxITrqTSCQQk3QUFhamp6frr+IDgMWAgAQoQFRfbchvNybRqvoq5RobGz/6\n6KOVK1dS3REAzAgCEqAGrr7aWntBJxE8JCSESASH6quEpKSkyMhI8q2XwKwKCgq+/fbby5cvd3sH\nk2HTVAEEJEAZXH1VvyK4WCwmJ91ZXkwqLy+/dOkSuaW0tPSHH34oLCzUaDS45eTJk2vWrFmzZs3O\nnTtPnTpVWVkZGRlp6GDA9CIiIiZNmrRx48bAwMCwsDD9e2M63MGUpFJzrLRLT3CjFqCSrWe4Rql4\nVJ6js/Z5dHQ0XlvW8iqCq9XqxMREDocTGBiIW7Zt25aeni4QCBQKhZ+fX0ZGBpfLFQgEwcHBCCFn\nZ+e0tDSFQhEWFtbQ0HD//v1NmzZt3LiR0jdhyc6cOZOTk1NQUODn55ednR0ZGVlYWDh69OjO72Bi\ncjkKDUUW9CdgDMXFXXsFrBjLROSK4GKx2Kw/q9dWjF23bl1ISIhQKFy+fDlukclkIpHo0KFDWq22\npKTEx8fn8OHDOq+qqKgoLS0tLS3dvXt3TExMRUWF/pHZVhbafL799tvFixfjbXx2np+f36UdTEgo\nFD5ebNdEKyzT/GNlS0CiugugO2QyGVG1oReWPO+FcZKdnb1v376oqCgiIGVnZ48ePVqtVuOHMTEx\n7733Xnsv/+GHH2JjYw0+JWxjqu9eLP+rqaqqSk5O9vPzmzFjBvHpdGkHk3gSkPh8bW5u9w5CfN/q\nnW9dPQFTdoAu7p2ehBAi1wXHSXcCgQAhhK8q4cX9mCsiIgIhpFAoiEnIO3fuuLu7E3fyDx48uKys\nrL2Xz5w5c+bMme09S+eSMCan0Wj++OOPhoYGLy8vJycnkx//3r17ubm51dXVzs7OVVVVbm5uXd3B\nZDIyUEwMkstRTEz3Ju5iY2NjY2PxNs1rNkJSA6CLvhOz9BuJ6qvIQhPBNRoNl8slHlpbW8NS2cY9\nePDg1Vdf7devn0gkGjt2rLOz88yZM69evdr5I9TX13M4nM2bNxvZRyQSHT58uLi4+M8//0xLS+vG\nDiYjFiM8dy2XW3zGHQQkQBccBw/9ZZPQ00l3lpcIzuPxyPe6KpVKGxsbCvtDczU1NQEBAfv371+4\ncGF2dnZmZubixYtzc3OnTp3apYGBJ4gMPrVs2bKpU6fi7T59+owaNUrn1LPDHUyv7TsZkkqRxX0n\nI4OABBjAgquvurm53b59u6mpCT8sKSlxd3fv3qHYsMbK5s2bS0tLU1NT09PTIyIiIiMj9+/f/+67\n71ZXV+/cubPj13fC+PHj8/Ly0tPTGxoajh49+uOPP+J0x1WrVmVmZhrZwYz4/McxCU/cdQsz1lih\n9hJW76D5dTygQ3lzR/2poJa758mNvZB012vjZPPmzURSQ3V19ciRI+Pj4+/evZuVlSUUCnO7de2a\nDVl2DQ0NdnZ2vr6+Ou0PHz5cuHBhXFxcJ49TV1eHEHr77bcjIiL69Onj4OAwb968qqoq/KxarV61\nahVeu8jGxiYuLg7nLCCEVqxYYWQHc3jqUwgJ6XnGHQ0/VjIISICOcExSN5aTG82ddNdr4+TTTz8l\nApJWqz169GhAQIBQKPT29t66dWv3jsmGgFRQUIAQSkxM7OFxcEBCCA0dOnTt2rVTpkxBCC1atIi8\nz6NHj27fvt3S0tLeQTrcwSSe+hRksp5n3NHwYyWDgAToSN1Yfv/sKwZjEnFyb/KYROE4UavVlZWV\nPfm/GxsCUlZWFkJo7969PTwODkiurq7379/HLSNGjHB3d+9xB01P91PIyHgSk0xyQJqBa0iAjp5U\nX9WrCE7EJEtKuuNwOC4uLjwej+qOtEtVXW7wn84O5tsfIYTrKpkqCzE8PLxv3754e9KkScRpE61Z\nesYd3IcEaApXX713elJj4VpH/21EO04Ex+l2MTExFC55TjcpKSnE7SYm15B3oPbAdv124aG/8IZs\n5Tj9hybcHyHk5eWFEDJYRyoxMVEul6enp3f8Ttq4uLgQ20xa0TUjAwkECCEklaLgYNR2YbVDKSkp\nqamp5uuXaVB9itYbaH6WCoxouXu+9ju+8uYOnXacdIfazplM8rMYPU7MPWXXcue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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% Robin boundary condition.\n",
    "fprintf('Robin boundary condition. \\n');\n",
    "pde = sincosRobindata3;\n",
    "mesh.bdFlag = setboundary3(node,elem,'Robin');\n",
    "femPoisson3(mesh,pde,option);"
   ]
  },
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   "source": [
    "## Conclusion\n",
    "\n",
    "The optimal rate of convergence of the H1-norm (2nd order) and L2-norm\n",
    "(3rd order) is observed. Superconvergence between discrete functions\n",
    "$\\| \\nabla u_I - \\nabla u_h \\|$ is only 2.5 order.\n",
    "\n",
    "For Neumann problem, the maximum norm is only 2.6 not optimal. \n",
    "\n",
    "MGCG converges uniformly in all cases."
   ]
  }
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     "text": "MetaKernel Magics",
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